A garnet single crystal containing an Fe element is widely used in magnetostatic wave (hereinafter abbreviated as MSW) devices, such as a delay line filter, an oscillator, and a nonlinear device. In particular, a Y.sub.3 Fe.sub.5 O.sub.12 (yttrium iron garnet; hereinafter referred to as YIG) single crystal is frequently used because it has an extremely small ferromagnetic half power width (.DELTA.H) to reduce a difference between an input signal and an output signal when used as an MSW device. A YIG single crystal is usually obtained by liquid phase epitaxial growth on a Gd.sub.3 Ga.sub.5 O.sub.12 (gadolinium gallium garnet; hereinafter referred to as GGG) substrate, the crystallographic plane azimuth of which is a (111) plane.
When a magnetostatic forward volume wave (MSFVW) mode is used in an MSW device using a garnet single crystal, the operating frequency of the device is represented by equation (1): EQU .omega.=Y(Hex-N.multidot.4.pi.Ms) (1)
wherein .omega. is a frequency; Y is a gyromagnetic ratio: Hex is an applied magnetic field; N is a coefficient of a diamagnetic field; and 4.pi.Ms is a saturation magnetization.
As is apparent from equation (1), an operating frequency can be controlled by an applied magnetic field and a saturated magnetic field. The frequency of an MSW device has thus been reduced by reducing the saturation magnetization by using an Fe-containing garnet single crystal film grown on a GGG substrate having a (111) plane.
On the other hand, where a magnetostatic surface wave (MSSW) mode is used, the operating frequency of the device can be represented by equation (2): EQU .omega.=Y{Hi(Hi+4.pi.Ms)}.sup. 1/2 ( 2)
wherein .omega., Y is, and 4.pi.Ms are as defined above; and Hi is an internal magnetic field.
Taking the influences of an anisotropic magnetic field and a saturated magnetic field into consideration, the anisotropic magnetic field is included in the formula representing the inner magnetic field as represented by equation (3): EQU Hi=Hex=N.multidot.4.pi.Ms+Ha (3)
wherein Hi, Hex, and N.multidot.4.pi.Ms are as defined above; and Ha is an anisotropic magnetic field.
In the case of using an MSSW mode, the diamagnetic field coefficient N becomes zero when a magnetic field is applied in parallel with the magnetic garnet single crystal film. Accordingly, equation (3) may be converted to equation (4): EQU Hi=Hex+Ha (4)
wherein Hi, Hex, and Ha are as defined above.
Equation (4) indicates that certain magnetic field exists inside the magnetic garnet single crystal film even if Hex is zero. Substitution of equation (4) for Hi in equation (2) gives equation (5): EQU .omega.=Y(Hex+Ha)(Hex+Ha+4.pi.Ms).sup. 1/2 ( 5)
wherein .omega., Y, Hex, Ha, and 4.pi.Ms are defined as above.
As can be understood from equations (4) and (5), when an MSSW mode is used, the lowest frequency .omega. in the propagation band cannot be controlled simply by reducing the saturation magnetization (4.pi.Ms), and it is also necessary to reduce the anisotropic magnetic field (Ha) for frequency control.